Application of FEM with Piecewise Mittag-Leffler Functions Basis for the Linear Elasticity Problem in Materials with Fractal Structure

In this paper, a fractional-order model of the gas film is proposed for the dynamic characteristics of an air bearing. Based on the dynamic characteristics common between gas film and viscoelastic body, the idea of the fractional-order equivalent modeling of the dynamic characteristics of the gas film is presented to improve the modeling accuracy. Four fractional-order gas film (FOGF) models are introduced based on generalization of traditional viscoelastic models. The analysis of the characteristics of the FOGF models shows that the FOGF model can capture more complex dynamic characteristics and fit the real dynamic data of the gas film better than traditional models. A genetic algorithm particle swarm optimization (GA-PSO) method is used for parameter identification of the proposed models. The experimental results tested on the air bearing motion platform show that the FOGF models are superior in accuracy to the traditional equivalent models for the gas film. In particular, the fractional-order Maxwell gas film (FOMGF) model has the best capture accuracy compared to the other FOGF models and traditional models.

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Boundary Value Problem of Space-Time Fractional Advection Diffusion Equation

Mahmoud

Aleroev

2022

Mathematics

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In this article, the analytical and numerical solution of a one-dimensional space-time fractional advection diffusion equation is presented. The separation of variables method is used to carry out the analytical solution, the basis of the system eigenfunction and their corresponding eigenvalue for basic equation is determined, and the numerical solution is based on constructing the Crank-Nicolson finite difference scheme of the equivalent partial integro-differential equations. The convergence and unconditional stability of the solution are investigated. Finally, the numerical and analytical experiments are given to verify the theoretical analysis.

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Application of FEM with Piecewise Mittag-Leffler Functions Basis for the Linear Elasticity Problem in Materials with Fractal Structure

Cited by 3 publications

References 14 publications

Parallel Algorithm for Numerical Modeling of Anisotropic Heat and Mass Transfer in Fractal Media

Parallel Algorithm for Numerical Modeling of Anisotropic Heat and Mass Transfer in Fractal Media

Fractional-Order Gas Film Model

Boundary Value Problem of Space-Time Fractional Advection Diffusion Equation

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